Problem: Solve for $x$ and $y$ using elimination. ${-5x+6y = 15}$ ${3x-3y = -3}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${-5x+6y = 15}$ $6x-6y = -6$ Add the top and bottom equations together. ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-5x+6y = 15}\thinspace$ to find $y$ ${-5}{(9)}{ + 6y = 15}$ $-45+6y = 15$ $-45{+45} + 6y = 15{+45}$ $6y = 60$ $\dfrac{6y}{{6}} = \dfrac{60}{{6}}$ ${y = 10}$ You can also plug ${x = 9}$ into $\thinspace {3x-3y = -3}\thinspace$ and get the same answer for $y$ : ${3}{(9)}{ - 3y = -3}$ ${y = 10}$